Artificial　optoelectronic　synapses　have　drawn　tremendous　attention　in　neuromorphic　computing　due　to　their　exceptional　properties　of　incorporating　optical-sensing　and　synaptic　functions.　However,　the　complex　fabrication　processes　and　device　architectures　greatly　limit　their　applications.　More　importantly,　artificial　neural　networks　(ANNs)　commonly　implemented　with　optoelectronic　synapses　cannot　take　full　advantage　of　the　time-dependent　data　of　synaptic　devices,　resulting　in　defective　accuracies.　Here,　facile　two-terminal　optoelectronic　synapses　based　on　topological　insulator　Sb2Te3　films　are　fabricated,　which　exhibit　significant　photocurrent　responses,　owing　to　the　efficient　light-matter　interaction　in　bulk　and　the　topological　surface　state　of　Sb2Te3.　The　performance　of　Sb2Te3　devices　can　be　tuned　both　optically　and　electrically.　Typical　characteristics　of　synapses,　such　as　paired-pulse　facilitation,　short-term　memory,　long-term　memory,　and　learning　behavior,　have　been　demonstrated.　With　the　establishment　of　recurrent　neural　networks　(RNNs)　that　are　committed　to　processing　temporal　data,　the　as-fabricated　synapse　devices　are　employed　for　binary　image　recognition　of　handwritten　numbers　＂0＂　and　＂1＂.　The　recognition　accuracy　of　RNNs　can　reach　as　high　as　100%,　which　is　dramatically　higher　than　those　of　ANNs.　The　effective　employment　of　temporal　data　with　RNNs　ensured　high　recognition　accuracy.　These　Sb2Te3　optoelectronic　synapses　with　RNNs　indicate　the　great　potential　for　developing　high-performance　brain-inspired　neuromorphic　computing.